For comprehensive analytical purposes, I think in terms of 3 main swing model levels.

1- MECHANICAL. Best model is Mankin CHP and TORQUE

2-BIOMECHANICAL. Best model is kinetic link/chain where most important determinant of body motion pattern is how the arms are connected to the torso and where the most important factor is loading of the torso by coil/twist ending with a last quick controllable stretch/coil for adjustment. Names for this would be "x-factor stretch" or "cusp". Best
described in golf.

3- KINESIOLOGICAL, or joint motion sequence/synch. Best upper body explanation is in throwing and also applies to the swing, see HODGE, BIOMECHANICBASEBALL. You may remember Hodge from discussions at Hudgen's site years ago.

The best lower body info is from Chris Yeager, see:

http://www.dryeagersbaseball.com/

"Weight shift" has most to do with level 2/biomechanics and with lower body/hip motion that supports the upper body.

The conversion of kinetic link/soft tissue elasticity/stretch/muscular force production and sequence of bone/joint configuration is best understood in golf.

The most similar golf swing is the "2 plane" golf swing as described best by Jim Hardy, PLANE TRUTH FOR GOLFERS. This is also the best reference for differentiating the 1 and 2 plane patterns of the swing.

"Weight shift" is primarily concerned with the creation of x-factor stretch and adjustment as described here, for example by Jim McClean who originally stressed only separation/"x-factor", but now stresses "x-factor stretch in the downswing" in which weight shift plays a key role:

http://www.golfdigest.com/instruction/swing/2008/01/mclean_xfactor

This emphasis on "x-factor stretch" is the same thing Zig's company was the first to highlight in research published in 2000.

Lower body action is probably best explained by understanding hip motion as described in golf, see especially the Jim Hardy DVD, SECRETS FROM THE PLANE TRUTH VAULT #5, "How the hips work in the golf swing".

Describing hip action is VERY hard to simplify, but Hardy's approach is the best I have seen.

Again, in the mlb hitting pattern, the hip motion is much like that of the 2 plane golf swing. The hip motion of the one plane golf swing is very different as is the overall 1 plane pattern. Hip motion involves where center is and when and how the weight is carried on the feet. Yeager's info is the best for understanding the MLB action that has to fit into the
big picture.

The shift of the weight is associated with the stretching of core muscles so that they can unload quickly in the right direction. This amounts to the storage and quick release of energy whether you want to think of this as primarily a momentum creation or transfer or
conversion or not. It is also intimately involved with biomechanics, not just mechanics.